Definition:Biadditive Mapping
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Definition
Let $M, N, P$ be abelian groups.
Let $M \times N$ be the cartesian product.
A biadditive mapping $f : M \times N \to P$ is a mapping such that:
- $\forall m_1, m_2 \in M : \forall n \in N: \map f {m_1 + m_2, n} = \map f {m_1, n} + \map f {m_2, n}$
- $\forall m \in M: \forall n_1, n_2 \in N: \map f {m, n_1 + n_2} = \map f {m, n_1} + \map f {m, n_2}$
Also known as
A biadditive mapping is also known as a $\Z$-bilinear mapping. See Correspondence between Abelian Groups and Z-Modules.
Also see
Sources
- 1974: N. Bourbaki: Algebra I: Chapter $\text {II}$. Linear Algebra $\S 3$. Tensor Products. $1$. Tensor product of two modules